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Smart antennas have been studied extensively for use in cellular radio base station applications. Recently however, low cost array technologies have suggested that adaptive antennas may soon be cost effective for mobile ad hoc networks. In this paper we consider the potential use of adaptive antenna arrays in networks using protocols based on the IEEE 802.11 distributed coordination function (DCF). In the system under study, omnidirectional RTS/CTS exchanges are used to initiate array-mode data packet transmissions. Several variations on the basic protocol are considered. When two stations communicate using their antenna arrays, the ensuing gain across the link can be very large. In many cases the transmit power can be significantly reduced while still maintaining a sufficient link margin. We show that this reduction in power is a key factor in improving the capacity of an ad hoc network. Results are presented for various parameters which show how the capacity of the system scales with the size of the system. Significant capacity improvements are possible compared with a network using conventional IEEE 802.11 protocols. In our simulations a relatively inexpensive circular antenna array configuration is used with a fairly modest number of elements.